Chapter 8, Problem 8.93LM

Two independent random samples are taken from two populations. The results of these samples are summarized in the next table.

Sample 1	Sample 2
n1 = 135	n2 = 148
${\bar{x}}_1=12.2$	${\bar{x}}_2=8.3$
$s_1^2=2.1$	$s_2^2=3.0$

Form a 90% confidence interval for (μ₁ – μ₂).

Test H₀: (μ₁ – μ₂) = 0 against H_a : (μ₁ – μ₂) ≠ 0 by comparing α = .01 with the p-value of the test.

What sample sizes would be required if you wish to estimate (μ₁ – μ₂) to within .2 with 90% confidence? Assume that n₁ = n₂.